Fixed point theorems for weak, partial, Bianchini, and Chatterjea–Bianchini contractions in semimetric spaces with triangle functions

This paper advances a line of research in fixed point theory initiated by M. Bessenyei and Z. Páles. The consideration is based on their introduction of the triangle function concept in [J. Nonlinear Convex Anal, Vol 18 (3), 515–524 (2017)]. By applying this concept, the study revises several well-known fixed point theorems in metric spaces, extending their applicability to semimetric spaces with triangle functions. The paper focuses on general theorems involving weak, partial, Bianchini, and Chatterjea–Bianchini contractions and derives corollaries relevant to metric spaces, b-metric spaces, ultrametric spaces, and distance spaces with power triangle functions. Notably, several new and interesting findings emerge in the context of weak and partial contractions.